Acoustic surface waves of the Rayleigh type near an impedance cone

The famous Maliuzhinets explicit solution gives possibility to study surface waves propagating from the edge singularity of an impedance wedge. The problem of diffraction by a circular impedance cone can hardly be solved in an explicit form. Nevertheless, recent progress enables us to investigate the surface waves of the Rayleigh type and the conditions of their excitation in the vicinity of the impedance conical surface. We consider the excitation of the acoustic surface waves. The scalar surface waves exist in the vicinity of the surface provided the imaginary part of the impedance has the appropriate sign. We also study the Weyl-Van-der-Pol phenomenon in the scalar problem. This phenomenon implies interference of the surface waves with the spherical wave propagating from the vertex for sufficiently small value of the surface impedance.